Average Error: 6.1 → 0.5
Time: 3.0s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.995469952665014041540810221972499392166 \cdot 10^{202}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.995469952665014041540810221972499392166 \cdot 10^{202}\right):\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{else}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r320321 = x;
        double r320322 = y;
        double r320323 = z;
        double r320324 = t;
        double r320325 = r320323 - r320324;
        double r320326 = r320322 * r320325;
        double r320327 = a;
        double r320328 = r320326 / r320327;
        double r320329 = r320321 - r320328;
        return r320329;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r320330 = y;
        double r320331 = z;
        double r320332 = t;
        double r320333 = r320331 - r320332;
        double r320334 = r320330 * r320333;
        double r320335 = -inf.0;
        bool r320336 = r320334 <= r320335;
        double r320337 = 2.995469952665014e+202;
        bool r320338 = r320334 <= r320337;
        double r320339 = !r320338;
        bool r320340 = r320336 || r320339;
        double r320341 = x;
        double r320342 = a;
        double r320343 = r320330 / r320342;
        double r320344 = r320343 * r320333;
        double r320345 = r320341 - r320344;
        double r320346 = r320334 / r320342;
        double r320347 = r320341 - r320346;
        double r320348 = r320340 ? r320345 : r320347;
        return r320348;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.1
Target0.8
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -inf.0 or 2.995469952665014e+202 < (* y (- z t))

    1. Initial program 39.5

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.6

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)}\]

    if -inf.0 < (* y (- z t)) < 2.995469952665014e+202

    1. Initial program 0.4

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.995469952665014041540810221972499392166 \cdot 10^{202}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))